def slow_coord_to_index(target,lens):
"""
Slow but simple way of converting coords to indices
Uses C-style indexing; this means the last coordinate
changes most freqently.
For an (P,Q,R) matrix:
0 0 0 -> 0
0 0 1 -> 1
0 0 2 -> 2
...
p q r -> r + R*q + (R*Q)*p
"""
assert is_vect(target)
assert is_int(target)
assert is_vect(lens)
assert is_int(target)
assert target.shape == lens.shape
(D,) = lens.shape
idx = 0
mult = 1
for d in xrange(D-1,-1,-1):
idx += mult * target[d]
mult *= lens[d]
return idx
def even_slower_coord_to_index(target,lens):
assert is_vect(target)
assert is_int(target)
assert is_vect(lens)
assert is_int(target)
assert target.shape == lens.shape
N = np.prod(lens)
C = np.reshape(np.arange(N),lens) # Should be row-major ordering
idx = tuple(target.astype(np.integer))
return C[idx]
def indices_to_coords(self,indices):
# Converts indices to coordinates
assert is_vect(indices)
assert is_int(indices)
(N,) = indices.shape
D = len(self.coef)
# Does the hard work
raw_coords = np.empty((N,D))
res = indices
for d in xrange(D):
(coord,res) = divmod(res,self.coef[d])
raw_coords[:,d] = coord
# OOB indices mapped to NAN
oob_mask = self.are_indices_oob(indices)
raw_coords[oob_mask,:] = np.nan
oob_indices = self.indices_to_oob_indices(indices,oob_mask)
oob = OutOfBounds()
oob.build_from_oob_indices(oob_indices,D)
coords = Coordinates(raw_coords,oob)
assert coords.check()
return coords
def build_from_points(self,grid,points):
assert is_mat(points)
(N,D) = points.shape
self.dim = D
self.num = N
self.shape = (N,D)
low = grid.get_lower_boundary()
high = grid.get_upper_boundary()
# What boundary is violated;
# -1 lower boundary,
# +1 upper boundary
U = sps.csc_matrix(points > high,dtype=np.integer)
L = sps.csc_matrix(points < row_vect(low),dtype=np.integer)
self.data = U - L
# Mask of same
self.mask = np.zeros(N,dtype=bool)
oob_rows = self.data.nonzero()[0]
self.mask[oob_rows] = True
assert isinstance(self.mask,np.ndarray)
assert (N,) == self.mask.shape
# Sanity check
assert np.all(self.mask == grid.are_points_oob(points))
# Pre-offset oob node or cell indices
self.indices = self.find_oob_index()
assert is_vect(self.indices)
assert np.all(np.isnan(self.indices) == ~self.mask)
assert self.check()
def indices_to_oob_indices(self,indices,oob_mask=None):
assert is_vect(indices)
assert is_int(indices)
# Identify oob indices
if oob_mask is None:
oob_mask = self.are_indices_oob(indices)
assert is_vect(oob_mask)
assert oob_mask.shape == indices.shape
# Subtract offset, so least oob index is 0
oob_indices = indices - self.get_num_spatial_nodes()
# Nan-out any normal index location
oob_indices[~oob_mask] = np.nan
return oob_indices
def cell_indices_to_mid_points(self,cell_indices):
assert is_vect(cell_indices)
low_points = cell_indices_to_low_points(self,cell_indices)
mid_points = low_points + row_vect(0.5 * self.delta)
assert is_mat(mid_points)
assert mid_points.shape[0] == cell_indices.shape[0]
return mid_points
def cell_indices_to_vertex_indices(self,cell_indices):
assert is_vect(cell_indices)
cell_coords = self.cell_indexer.indices_to_coords(cell_indices)
assert isinstance(cell_coords,Coordinates)
vertex_indices = self.cell_coords_to_vertex_indices(cell_coords)
assert is_mat(vertex_indices) # (N x 2**D) matrix
return vertex_indices
def cell_indices_to_low_points(self,cell_indices):
assert is_vect(cell_indices)
cell_coords = self.cell_indexer.indices_to_coords(cell_indices)
assert isinstance(cell_coords,Coordinates)
assert cell_coords.check()
low_points = self.cell_coords_to_low_points(cell_coords)
assert is_mat(low_points)
assert cell_coords.shape == low_points.shape
return low_points
def points_to_cell_indices(self,points):
assert is_mat(points)
(N,D) = points.shape
cell_coords = self.points_to_cell_coords(points)
assert isinstance(cell_coords,Coordinates)
assert (N,D) == cell_coords.shape
cell_indices = self.cell_indexer.coords_to_indices(cell_coords)
assert is_vect(cell_indices)
assert (N,) == cell_indices.shape
return cell_indices
def check(self):
assert isinstance(self.data,sps.spmatrix)
assert is_vect(self.mask)
assert is_vect(self.indices)
(N,D) = self.shape
assert N == self.num
assert D == self.dim
assert (N,D) == self.data.shape
assert (N,) == self.mask.shape
assert (N,) == self.indices.shape
nz_rows = np.unique(self.data.nonzero()[0])
assert np.all(self.mask[nz_rows])
assert np.all(np.isnan(self.indices) == ~self.mask)
assert not np.any(np.isnan(self.indices[self.mask]))
assert np.all(np.isnan(self.indices[~self.mask]))
assert np.all(self.indices[self.mask] >= 0)
assert np.all(self.indices[self.mask] < 2*D)
return True
def node_indices_to_node_points(self,node_indices):
assert is_vect(node_indices)
(N,) = node_indices.shape
node_coords = self.node_indexer.indices_to_coords(node_indices)
assert isinstance(node_coords,Coordinates)
oob = node_coords.oob
C = node_coords.coords
assert np.all(np.isnan(C[oob.mask,:]))
node_points = row_vect(self.lower_bound) + C * row_vect(self.delta)
assert is_mat(node_points)
assert np.all(np.isnan(node_points[oob.mask,:]))
assert node_coords.shape == node_points.shape
return node_points
def build_from_oob_indices(self,indices,D):
"""
Indices should be np.nan if not oob.
Max spatial index should be already subtracted off, so indices should
be integers in [0,2*D).
"""
assert is_vect(indices)
assert is_int(indices) # ignore nan
oob_mask = ~np.isnan(indices)
assert not np.any(indices[oob_mask] < 0)
assert not np.any(indices[oob_mask] >= 2*D)
(N,) = indices.shape
self.dim = D
self.num = N
self.shape = (N,D)
self.mask = oob_mask # Binary mask
self.indices = np.empty(N)
self.indices.fill(np.nan)
self.indices[oob_mask] = indices[oob_mask] # Cache of the indices
# Go through the non nan indices, unpack into data
data = sps.lil_matrix((N,D),dtype=np.integer)
for d in xrange(D):
# Even indices
mask = (self.indices == 2*d)
data[mask,d] = -1
# Odd indices
mask = (self.indices == 2*d+1)
data[mask,d] = 1
self.data = data.tocsc()
assert self.check()
